On a distant inhabited planet in our Galaxy, observing astronomers do not have spectral instruments, but there is a photometer

On a distant inhabited planet in our Galaxy, observing astronomers do not have spectral instruments, but there is a photometer that records changes in the brightness of the stars, quantitatively equal to the brightness of one star 20m. At what distance from the Sun with the help of such a device can one establish the existence of a planetary system near the Sun?

With such a photometer at their disposal, the inhabitants of a distant planet could try to register a fall in the brightness of the Sun, associated with the passage of the largest planet in the solar system, Jupiter, across its disk. The diameter of this planet is 9.7 times smaller than that of the Sun, and during the passage the brightness of the Sun will decrease by about one hundredth. If the brightness of the Sun on this planet is 100 times brighter than that of a 20m star, that is, 15m, then the problem of detecting a planetary system near the Sun could well be solved. Taking into account that the absolute stellar magnitude of the Sun is slightly brighter than 5m, this could happen at a distance of up to 1 kpc from the Sun, but, alas, only near the plane of Jupiter’s orbit.

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